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CS425: Algorithms for Web Scale Data
Most of the slides are from the Mining of Massive Datasets book.
These slides have been modified for CS425. The original slides can be accessed at: www.mmds.org
Customer X
Buys Metallica CD
Buys Megadeth CD
Customer Y Does search on Metallica
Recommender system suggests Megadeth from data collected about customer X
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 2
Items
Search Recommendations
Products, web sites,
blogs, news items, …
3J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Examples:
Shelf space is a scarce commodity for traditional retailers Also: TV networks, movie theaters,…
Web enables near-zero-cost dissemination of information about products From scarcity to abundance
More choice necessitates better filters Recommendation engines
How Into Thin Air made Touching the Voida bestseller: http://www.wired.com/wired/archive/12.10/tail.html
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 4
Source: Chris Anderson (2004)
5J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 6
Read http://www.wired.com/wired/archive/12.10/tail.html to learn more!
Editorial and hand curated
List of favorites
Lists of “essential” items
Simple aggregates
Top 10, Most Popular, Recent Uploads
Tailored to individual users
Amazon, Netflix, …
7J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
X = set of Customers S = set of Items
Utility function u: X × S R
R = set of ratings
R is a totally ordered set
e.g., 0-5 stars, real number in [0,1]
8J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
0.4
10.2
0.30.5
0.21
Avatar LOTR Matrix Pirates
Alice
Bob
Carol
David
9J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
(1) Gathering “known” ratings for matrix How to collect the data in the utility matrix
(2) Extrapolate unknown ratings from the known ones Mainly interested in high unknown ratings We are not interested in knowing what you don’t like
but what you like
(3) Evaluating extrapolation methods How to measure success/performance of
recommendation methods
10J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Explicit
Ask people to rate items
Doesn’t work well in practice – people can’t be bothered
Implicit
Learn ratings from user actions
E.g., purchase implies high rating
What about low ratings?
11J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Key problem: Utility matrix U is sparse
Most people have not rated most items
Cold start:
New items have no ratings
New users have no history
Three approaches to recommender systems:
1) Content-based
2) Collaborative
3) Latent factor based
12J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
This lecture
Main idea: Recommend items to customer xsimilar to previous items rated highly by x
Example: Movie recommendations
Recommend movies with same actor(s), director, genre, …
Websites, blogs, news
Recommend other sites with “similar” content
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 14
likes
Item profiles
Red
Circles
Triangles
User profile
match
recommendbuild
15J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
For each item, create an item profile
Profile is a set (vector) of features
Movies: author, title, actor, director,…
Text: Set of “important” words in document
How to pick important features?
Usual heuristic from text mining is TF-IDF(Term frequency * Inverse Doc Frequency)
Term … Feature
Document … Item
16J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
fij = frequency of term (feature) i in doc (item) j
ni = number of docs that mention term iN = total number of docs
TF-IDF score: wij = TFij × IDFi
Doc profile = set of words with highest TF-IDF scores, together with their scores
17J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Note: we normalize TF
to discount for “longer”
documents
18CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Two Types of Document Similarity
In the LSH lecture: Lexical similarity Large identical sequences of characters
For recommendation systems: Content similarity Occurrences of common important words
TF-IDF score: If an uncommon word appears more frequently in two documents, it contributes to similarity.
Similar techniques (e.g. MinHashing and LSH) are still applicable.
19CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Representing Item Profiles
A vector entry for each feature Boolean features
e.g. One bool feature for every actor, director, genre, etc.
Numeric features
e.g. Budget of a movie, TF-IDF for a document, etc.
We may need weighting terms for normalization of features
Spielberg Scorsese Tarantino Lynch Budget
Jurassic Park 1 0 0 0 63M
Departed 0 1 0 0 90M
Eraserhead 0 0 0 1 20K
Twin Peaks 0 0 0 1 10M
20CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
User Profiles – Option 1
Option 1: Weighted average of rated item profiles
JurassicPark
MinorityReport
Schindler’s List
Departed Aviator Eraserhead
TwinPeaks
User 1 4 5 1 1
User 2 2 3 1 5 4
User 3 5 4 5 5 3
Utility matrix (ratings 1-5)
Spielberg Scorcese Lynch
User 1 4.5 0 1
User 2 2.5 1 4.5
User 3 4.5 5 3
User profile(ratings 1-5)
Missing scores
similar to
bad scores
21CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
User Profiles – Option 2 (Better)
Option 2: Subtract average values from ratings first
JurassicPark
MinorityReport
Schindler’s List
Departed Aviator Eraserhead
TwinPeaks
Avg
User 1 4 5 0 1 1 2.75
User 2 2 3 1 5 4 3
User 3 5 4 5 5 3 4.4
Utility matrix (ratings 1-5)
22CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
User Profiles – Option 2 (Better)
Option 2: Subtract average values from ratings first
JurassicPark
MinorityReport
Schindler’s List
Departed Aviator Eraserhead
TwinPeaks
Avg
User 1 1.25 2.25 -1.75 -1.75 2.75
User 2 -1 0 -2 3 1 3
User 3 0.6 -0.4 0.6 0.6 -1.4 4.4
Utility matrix (ratings 1-5)
Spielberg Scorcese Lynch
User 1 1.75 0 -1.75
User 2 -0.5 -2 2
User 3 -0.1 0.6 -1.4
User profile
23CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Heuristic
Given: A feature vector for user U
A feature vector for movie M
Predict user U’s rating for movie M
Which distance metric to use?
Cosine distance is a good candidate Works on weighted vectors
Only directions are important, not the magnitude
The magnitudes of vectors may be very different in movies and users
24CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Reminder: Cosine Distance
Consider x and y represented as vectors in an n-dimensional space
cos 𝜃 =𝑥.𝑦
𝑥 .| 𝑦 |
The cosine distance is defined as the θ value Or, cosine similarity is defined as cos(θ)
Only direction of vectors considered, not the magnitudes
Useful when we are dealing with vector spaces
θ
xy
25CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Reminder: Cosine Distance - Example
cos 𝜃 =𝑥. 𝑦
𝑥 . | 𝑦 |=
0.2 + 0.2 − 0.1
0.01 + 0.04 + 0.01 . 4 + 1 + 1
=0.3
0.36= 0.5 θ = 600
Note: The distance is independent of vector magnitudes
θx = [0.1, 0.2, -0.1]
y = [2.0, 1.0, 1.0]
26CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Example
User and movie feature vectors
Actor 1 Actor 2 Actor 3 Actor 4
User U -0.6 0.6 -1.5 2.0
Movie 1 1 1 0 0
Movie 2 1 0 1 0
Movie 3 0 1 0 1
Predict the rating of user U for movies 1, 2, and 3
27CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Example
Actor 1 Actor 2 Actor 3 Actor 4 VectorMagn.
User U -0.6 0.6 -1.5 2.0 2.6
Movie 1 1 1 0 0 1.4
Movie 2 1 0 1 0 1.4
Movie 3 0 1 0 1 1.4
Predict the rating of user U for movies 1, 2, and 3
28CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Example
Actor 1 Actor 2 Actor 3 Actor 4 VectorMagn.
CosineSim
User U -0.6 0.6 -1.5 2.0 2.6
Movie 1 1 1 0 0 1.4 0
Movie 2 1 0 1 0 1.4 -0.6
Movie 3 0 1 0 1 1.4 0.7
Predict the rating of user U for movies 1, 2, and 3
29CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Example
Actor 1 Actor 2 Actor 3 Actor 4 VectorMagn.
CosineSim
CosineDist
User U -0.6 0.6 -1.5 2.0 2.6
Movie 1 1 1 0 0 1.4 0 900
Movie 2 1 0 1 0 1.4 -0.6 1240
Movie 3 0 1 0 1 1.4 0.7 460
Predict the rating of user U for movies 1, 2, and 3
30CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Example
Actor 1 Actor 2 Actor 3 Actor 4 VectorMagn.
CosineSim
CosineDist
Interpretation
User U -0.6 0.6 -1.5 2.0 2.6
Movie 1 1 1 0 0 1.4 0 900 Neither likes nor dislikes
Movie 2 1 0 1 0 1.4 -0.6 1240 Dislikes
Movie 3 0 1 0 1 1.4 0.7 460 Likes
Predict the rating of user U for movies 1, 2, and 3
31CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Content-Based Approach: True or False?
Need data on other users
False
Can handle users with unique tastes
True – no need to have similarity with other users
Can handle new items easily
True – well-defined features for items
Can handle new users easily
False – how to construct user-profiles?
Can provide explanations for the predicted recommendations
True – know which features contributed to the ratings
Likes Metallica,
Sinatra and Bieber
+: No need for data on other users
No cold-start or sparsity problems
+: Able to recommend to users with unique tastes
+: Able to recommend new & unpopular items
No first-rater problem
+: Able to provide explanations
Can provide explanations of recommended items by listing content-features that caused an item to be recommended
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 32
–: Finding the appropriate features is hard E.g., images, movies, music
–: Recommendations for new users How to build a user profile?
–: Overspecialization Never recommends items outside user’s
content profile
People might have multiple interests
Unable to exploit quality judgments of other users e.g. Users who like director X also like director Y
User U rated X, but doesn’t know about Y
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 33
Harnessing quality judgments of other users
Consider user x
Find set N of other users whose ratings are “similar” to x’s ratings
Estimate x’s ratings based on ratings of users in N
35J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
x
N
Let rx be the vector of user x’s ratings Jaccard similarity measure Problem: Ignores the value of the rating
Cosine similarity measure
sim(x, y) = cos(rx, ry) = 𝑟𝑥⋅𝑟𝑦
||𝑟𝑥||⋅||𝑟𝑦||
Problem: Treats missing ratings as “negative” Pearson correlation coefficient Sxy = items rated by both users x and y
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 36
rx = [*, _, _, *, ***]
ry = [*, _, **, **, _]
rx, ry as sets:
rx = {1, 4, 5}
ry = {1, 3, 4}
rx, ry as points:
rx = {1, 0, 0, 1, 3}
ry = {1, 0, 2, 2, 0}
rx, ry … avg.
rating of x, y
𝒔𝒊𝒎 𝒙, 𝒚 =σ𝒔∈𝑺𝒙𝒚
𝒓𝒙𝒔 − 𝒓𝒙 𝒓𝒚𝒔 − 𝒓𝒚
σ𝒔∈𝑺𝒙𝒚𝒓𝒙𝒔 − 𝒓𝒙
𝟐 σ𝒔∈𝑺𝒙𝒚𝒓𝒚𝒔 − 𝒓𝒚
𝟐
Intuitively we want: sim(A, B) > sim(A, C) Jaccard similarity: 1/5 < 2/4 Cosine similarity: 0.386 > 0.322
Considers missing ratings as “negative”
Solution: subtract the (row) mean
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 37
sim A,B vs. A,C:
0.092 > -0.559
Notice cosine sim. is
correlation when
data is centered at 0
𝒔𝒊𝒎(𝒙, 𝒚) =σ𝒊 𝒓𝒙𝒊 ⋅ 𝒓𝒚𝒊
σ𝒊 𝒓𝒙𝒊𝟐 ⋅ σ𝒊 𝒓𝒚𝒊
𝟐
Cosine sim:
From similarity metric to recommendations: Let rx be the vector of user x’s ratings Let N be the set of k users most similar to x
who have rated item i Prediction for item i of user x:
𝑟𝑥𝑖 =1
𝑘σ𝑦∈𝑁 𝑟𝑦𝑖
𝑟𝑥𝑖 =σ𝑦∈𝑁 𝑠𝑥𝑦⋅𝑟𝑦𝑖
σ𝑦∈𝑁 𝑠𝑥𝑦
Other options?
Many other tricks possible…38J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Shorthand:𝒔𝒙𝒚 = 𝒔𝒊𝒎 𝒙, 𝒚
39CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Rating Predictions
Prediction based on the top 2 neighbors who have also rated HP2
similarity of A
0.09
-0.56
0
Predict the rating of A for HP2:
Option 1: 𝑟𝑥𝑖 =1
𝑘σ𝑦∈𝑁 𝑟𝑦𝑖
rA,HP2 = (5+3) / 2 = 4
40CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Rating Predictions
Prediction based on the top 2 neighbors who have also rated HP2
similarity of A
0.09
-0.56
0
Predict the rating of A for HP2:
Option 2: 𝑟𝑥𝑖 =σ𝑦∈𝑁 𝑠𝑥𝑦⋅𝑟𝑦𝑖
σ𝑦∈𝑁 𝑠𝑥𝑦
rA,HP2 = (5 x 0.09 + 3 x 0) / 0.09 = 5
So far: User-user collaborative filtering Another view: Item-item
For item i, find other similar items
Estimate rating for item i based on ratings for similar items
Can use same similarity metrics and prediction functions as in user-user model
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 41
);(
);(
xiNj ij
xiNj xjij
xis
rsr
sij… similarity of items i and j
rxj…rating of user u on item j
N(i;x)… set items rated by x similar to i
121110987654321
455311
3124452
534321423
245424
5224345
423316
users
mo
vie
s
- unknown rating - rating between 1 to 5
42J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
121110987654321
455 ?311
3124452
534321423
245424
5224345
423316
users
- estimate rating of movie 1 by user 5
43J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
mo
vie
s
121110987654321
455 ?311
3124452
534321423
245424
5224345
423316
users
Neighbor selection:
Identify movies similar to
movie 1, rated by user 544J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
mo
vie
s
1.00
-0.18
0.41
-0.10
-0.31
0.59
sim(1,m)
Here we use Pearson correlation as similarity:
1) Subtract mean rating mi from each movie i
m1 = (1+3+5+5+4)/5 = 3.6
row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0]
2) Compute cosine similarities between rows
121110987654321
455 ?311
3124452
534321423
245424
5224345
423316
users
Neighbor selection:
Identify movies similar to
movie 1, rated by user 545J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
mo
vie
s
1.00
-0.18
0.41
-0.10
-0.31
0.59
sim(1,m)
Here we use Pearson correlation as similarity:
1) Subtract mean rating mi from each movie i
m1 = (1+3+5+5+4)/5 = 3.6
row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0]
2) Compute cosine similarities between rows
121110987654321
455 ?311
3124452
534321423
245424
5224345
423316
users
Compute similarity weights:
s1,3=0.41, s1,6=0.59
46J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
mo
vie
s
1.00
-0.18
0.41
-0.10
-0.31
0.59
sim(1,m)
121110987654321
4552.6311
3124452
534321423
245424
5224345
423316
users
Predict by taking weighted average:
r1.5 = (0.41*2 + 0.59*3) / (0.41+0.59) = 2.6
47J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
mo
vie
s
𝒓𝒊𝒙 =σ𝒋∈𝑵(𝒊;𝒙) 𝒔𝒊𝒋 ⋅ 𝒓𝒋𝒙
σ𝒔𝒊𝒋
Define similarity sij of items i and j Select k nearest neighbors N(i; x)
Items most similar to i, that were rated by x
Estimate rating rxi as the weighted average:
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 48
baseline estimate for rxi μ = overall mean movie rating bx = rating deviation of user x
= (avg. rating of user x) – μ bi = rating deviation of movie i
);(
);(
xiNj ij
xiNj xjij
xis
rsr
Before:
);(
);()(
xiNj ij
xiNj xjxjij
xixis
brsbr
𝒃𝒙𝒊 = 𝝁 + 𝒃𝒙 + 𝒃𝒊
49CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Example
The global movie rating is μ = 2.8i.e. average of all ratings of all users is 2.8
The average rating of user x is μx = 3.5
Rating deviation of user x is bx = μx – μ = 0.7i.e. this user’s avg rating is 0.7 larger than global avg
The average rating for movie i is μi = 2.6
Rating deviation of movie i is bi = μi – μ = -0.2i.e. this movie’s avg rating is 0.2 less than global avg
Baseline estimate for user x and movie i is 𝒃𝒙𝒊 = 𝝁 + 𝒃𝒙 + 𝒃𝒊 = 𝟐. 𝟖 + 𝟎. 𝟕 − 𝟎. 𝟐 = 𝟑. 𝟑
50CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Example (cont’d)
Items k and m: The most similar items to i that are also rated by x
Assume both have similarity values of 0.4
Assume:
rxk = 2 and bxk = 3.2 → deviation of -1.2
rxm = 3 and bxk = 3.8 → deviation of -0.8
);(
);()(
xiNj ij
xiNj xjxjij
xixis
brsbr
51CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Example (cont’d)
Rating rxi is the baseline rating plus the weighted avg of deviations of the most similar items’ ratings:
𝑟𝑥𝑖 = 3.3 +0.4× −1.2 +0.4×(−0.8)
0.4+0.4= 2.3
);(
);()(
xiNj ij
xiNj xjxjij
xixis
brsbr
0.41
8.010.9
0.30.5
0.81
Avatar LOTR Matrix Pirates
Alice
Bob
Carol
David
52J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
In practice, it has been observed that item-itemoften works better than user-user
Why? Items are simpler, users have multiple tastes
53CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Collaborating Filtering: True or False?
Need data on other users
True
Effective for users with unique tastes and esoteric items
False – relies on similarity between users or items
Can handle new items easily
False – cold start problems
Can handle new users easily
False – cold start problems
Can provide explanations for the predicted recommendations
User-user: False – “because users X, Y, Z also liked it”
Item-item: True – “because you also liked items i, j, k”
+ Works for any kind of item No feature selection needed
- Cold Start: Need enough users in the system to find a match
- Sparsity: The user/ratings matrix is sparse Hard to find users that have rated the same items
- First rater: Cannot recommend an item that has not been
previously rated New items, Esoteric items
- Popularity bias: Cannot recommend items to someone with
unique taste Tends to recommend popular items
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 54
Implement two or more different recommenders and combine predictions
Perhaps using a linear model
Add content-based methods to collaborative filtering
Item profiles for new item problem
Demographics to deal with new user problem
55J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
56CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Item/User Clustering to Reduce Sparsity
- Evaluation- Error metrics- Complexity / Speed
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 57
1 3 4
3 5 5
4 5 5
3
3
2 2 2
5
2 1 1
3 3
1
movies
users
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 58
1 3 4
3 5 5
4 5 5
3
3
2 ? ?
?
2 1 ?
3 ?
1
Test Data Set
users
movies
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 59
Compare predictions with known ratings Root-mean-square error (RMSE)
σ𝑥𝑖 𝑟𝑥𝑖 − 𝑟𝑥𝑖∗ 2
where 𝒓𝒙𝒊 is predicted, 𝒓𝒙𝒊∗ is the true rating of x on i
Another approach: 0/1 model Coverage: Number of items/users for which system can make predictions
Precision: Accuracy of predictions
Receiver operating characteristic (ROC) Tradeoff curve between true positives and false positives
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 60
Narrow focus on accuracy sometimes misses the point
Prediction Context
Prediction Diversity
61J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
62CS 425 – Lecture 8 Mustafa Ozdal, Bilkent University
Prediction Diversity Problem
In practice, we care only to predict high ratings:
RMSE might penalize a method that does well for high ratings and badly for others
Alternative: Precision at top k
63J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Expensive step is finding k most similar customers: O(|X|)
Too expensive to do at runtime
Could pre-compute
Naïve pre-computation takes time O(k ·|X|) X … set of customers
We already know how to do this!
Near-neighbor search in high dimensions (LSH)
Clustering
Dimensionality reduction
64J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
Leverage all the data
Don’t try to reduce data size in an effort to make fancy algorithms work
Simple methods on large data do best
Add more data
e.g., add IMDB data on genres
More data beats better algorithmshttp://anand.typepad.com/datawocky/2008/03/more-data-usual.html
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 65